Answer
$\phi = {q\over 24\epsilon_0}$
Work Step by Step
Surround the charge $q$ by 8 such cubes such that 4 cubes are above and 4 cubes are below and all are geometrically equivalent.
By guass law, the total flux would be
$\oint \vec{E}\cdot \vec{da} = {Q_{enc}\over \epsilon} = {q\over \epsilon}$
Let $\phi$ be the flux through the required surface.
There would be $4\times 6 $ such faces and all are geometrically equivalent. Hence, the flux through them would be same and summation of them would be the total flux.
Hence,
$\oint \vec{E}\cdot \vec{da} = {24 \phi} = {q\over \epsilon_0}$
$\therefore \phi = {q\over 24\epsilon_0}$
